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Statistics and Computing

, Volume 28, Issue 1, pp 61–75 | Cite as

On the generalization of the hazard rate twisting-based simulation approach

  • Nadhir Ben RachedEmail author
  • Fatma Benkhelifa
  • Abla Kammoun
  • Mohamed-Slim Alouini
  • Raul Tempone
Article
  • 248 Downloads

Abstract

Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. A naive Monte Carlo simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. An alternative approach is represented by the use of variance reduction techniques, known for their efficiency in requiring less computations for achieving the same accuracy requirement. Most of these methods have thus far been proposed to deal with specific settings under which the RVs belong to particular classes of distributions. In this paper, we propose a generalization of the well-known hazard rate twisting Importance Sampling-based approach that presents the advantage of being logarithmic efficient for arbitrary sums of RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of the proposed method with some existing techniques.

Keywords

Naive Monte Carlo Rare events Importance sampling Hazard rate twisting Logarithmic efficient Twisting parameter 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Computer, Electrical and Mathematical Science and Engineering (CEMSE) DivisionKing Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia

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